{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T21:55:35Z","timestamp":1757541335698},"reference-count":3,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":6798,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1988,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper solves the minimum augmentation problem for a given tree and positive integer k, that is, to make a tree k\u2010edge\u2010connected by adding the minimum number of edges. It is shown that the minimum number of edges is the least integer not less than a half of the deficiency of the tree which is defined as the sum of k\u2010(degree) over all the vertices whose degrees are less than k. The proof is constructive and gives a polynomial\u2010time algorithm for constructing such an augmentation.<\/jats:p>","DOI":"10.1002\/net.3230180104","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T22:50:01Z","timestamp":1178923801000},"page":"19-25","source":"Crossref","is-referenced-by-count":18,"title":["Minimum augmentation of a tree to a K\u2010edge\u2010connected graph"],"prefix":"10.1002","volume":"18","author":[{"given":"Shuichi","family":"Ueno","sequence":"first","affiliation":[]},{"given":"Yoji","family":"Kajitani","sequence":"additional","affiliation":[]},{"given":"Hajime","family":"Wada","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0205044"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0210019"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230160207"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230180104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230180104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T20:16:43Z","timestamp":1697919403000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230180104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,3]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1988,3]]}},"alternative-id":["10.1002\/net.3230180104"],"URL":"https:\/\/doi.org\/10.1002\/net.3230180104","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,3]]}}}